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 Trigonometry Trigonometry Math Forum

 July 31st, 2015, 01:17 AM #1 Newbie   Joined: Jun 2015 From: South Africa Posts: 27 Thanks: 0 Symmetry properties of graphs In each of the following cases find the least positive value of α for which: a) cos(α-θ)˚=sinθ˚ b) sin(α-θ)˚=cos(α+θ)˚ There are a whole bunch more... I did a) easily because obviously cos(90-θ)˚=sinθ˚, so α = 90. I'm struggling to work out b) though... Thanks for any help.  July 31st, 2015, 04:50 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 This is how I would do it. Simplifying $\sin(\alpha - \theta) = \cos(\alpha + \theta)$, we get $$\sin(\alpha - \theta) = \cos(\alpha + \theta)\\ \sin\alpha\cos\theta - \sin\theta\cos\alpha = \cos\alpha\cos\theta - \sin\alpha\sin\theta\\ \sin\alpha(\cos\theta + \sin\theta) = \cos\alpha(\cos\theta + \sin\theta)\qquad\qquad\qquad(1)$$ In cases where $\cos\theta + \sin\theta = 0$, equality holds trivially. Otherwise, $(1)$ can be simplified to $$\sin\alpha = \cos\alpha,$$ or, $$\tan\alpha = 1.$$ We now see that the answer is $\alpha = 45^\circ$ Tags graphs, properties, symmetry Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mared Algebra 1 January 27th, 2014 06:52 AM AfroMike Abstract Algebra 0 October 24th, 2013 06:49 AM MageKnight Applied Math 0 January 17th, 2013 10:38 PM ChristinaScience Algebra 3 October 2nd, 2011 10:42 AM

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